O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Chapter: Speed, Time and Distance, Exercise 1: Exercise

A motorist travelled $\frac{1}{2}$ of his journey at $60 \mathrm{km}/\mathrm{h}$ and completed the remaining $90 \mathrm{km}$ in $1\frac{1}{2}$ hours. If his average speed for the whole journey was $a \mathrm{km}/\mathrm{hr}$, then find the value of $a$.

A truck and a bus started off at $10:30 \mathrm{a}.\mathrm{m}.$ from opposite ends of a highway. The truck travelled at a speed of $40 \mathrm{km}/\mathrm{h}$ and the bus travelled at a speed of $54 \mathrm{km}/\mathrm{h}$. If they passed each other at $1 :00 \mathrm{p}.\mathrm{m}.$, then the length of the highway was $a \mathrm{km}$. Find the value of $a$.

A car started from Town $P$ and travelled towards Town $Q$ at $70 \mathrm{km}/\mathrm{h}$. At the same time a van started from Town $Q$ and travelled to Town $P$ at $60 \mathrm{km}/\mathrm{h}$. After $2\frac{3}{4}$ hours, they were $65 \mathrm{km}$ apart, still travelling towards each other. If the distance between the two towns is $x \mathrm{km}$, then find the value of $x$.

A car started from Town $P$ and travelled towards Town $Q$ at $70 \mathrm{km}/\mathrm{h}$. At the same time a van started from Town $Q$ and travelled to Town $P$ at $60 \mathrm{km}/\mathrm{h}$. After $2\frac{3}{4}$ hours, they were $65 \mathrm{km}$ apart, still travelling towards each other. After $x\frac{1}{4}$ hours of travel, they will cross each other. Find the value of $x$.

A train is booked to do the run between two places, $55 \mathrm{km}$ apart, in $1 \mathrm{hr} 20 \min$. If it travels for the first $30 \mathrm{km}$ at $36 \mathrm{km}$ per hour, at a speed of $x \mathrm{km}/\mathrm{hr}$ it must travel for the rest of the distance in order to complete the journey in time. Find the value of $x$.

Ajay walked at an average speed of $8 \mathrm{km}/\mathrm{hr}$ for $45$ minutes and then ran at an average speed of $12 \mathrm{km}/\mathrm{hr}$ for $40$ minutes. If his average speed for the whole journey was $x\frac{15}{17} \mathrm{km}/\mathrm{hr}$, then find the value of $x$.

Sujeet covers a distance in $40$ minutes if he drives at a speed of $60 \mathrm{km}/\mathrm{h}$ on an average. Find the speed at which he must drive to reduce the time of journey by $25\%$?

$A$ and $B$ are two stations $560 \mathrm{km}$ apart. A train starts from $A$ at $7 \mathrm{a}.\mathrm{m}.$ and travels towards $B$ at $80 \mathrm{km}/\mathrm{h}$. Another train starts from $B$ at $9 \mathrm{a}.\mathrm{m}.$ and travels towards $A$ at $120 \mathrm{km}/\mathrm{h}$. When will they meet each other?